What is the correct formula for updating the weights in a 1-single hidden layer neural network?
The correct formula for updating the weights between the hidden layer and the output layer is:
$$\Delta W_{j,k} = h_k \ \cdot \ o'_{j} \ \cdot \ (o_j - t_j),$$
where $h$ is the activated hidden layer and $o'$ is the derivative of output layer.
I found this formula in the book Artificial Intelligence: A Guide to Intelligent Systems by Michael Negnevitsky.